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https://ah.lib.nccu.edu.tw/handle/140.119/71418
題名: | Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation | 作者: | 陳隆奇 Chen, Lung-Chi Akira Sakai |
貢獻者: | 應數系 | 關鍵詞: | Long-range oriented percolation;Mean-field critical behavior;Limit theorem;Crossover phenomenon;Lace expansion;Fractional moments;60K35;82B27 | 日期: | 2009 | 上傳時間: | 13-Nov-2014 | 摘要: | We prove that the Fourier transform of the properly scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index α > 0 converges to e−C|k|α∧2 for some C∈(0,∞) above the upper-critical dimension dc≡2(α∧2) . This answers the open question remained in the previous paper (Chen and Sakai in Probab Theory Relat Fields 142:151–188, 2008). Moreover, we show that the constant C exhibits crossover at α = 2, which is a result of interactions among occupied paths. The proof is based on a new method of estimating fractional moments for the spatial variable of the lace-expansion coefficients. | 關聯: | Probability Theory and Related Fields, 145, 435-458 | 資料類型: | article |
Appears in Collections: | 期刊論文 |
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